Could someone explain me why, in America, when someone loses an election, he never represents himself again ?

It's because we have a two-party system, and parties don't like to nominate proven losers.

But there are rare exceptions. Nixon lost to John F. Kennedy in 1960, and came back eight years later and won.

And, of course, it's actually very common for a politician to run in multiple primaries. McCain lost the 2000 primary and was nominated in 2008; Romney lost the 2008 primary and was nominated in 2012.

That is not true. Nixon and Romney could never get the message. Nixon got very lucky because of the very unpopular Vietnam War and many liberals were very unhappy with the Democrat Party.

Candidates who do not get past he primary level will sometimes run again. IF you gain your political party's nomination the party and supporters put up so much money and effort it is unlikely they would support you again if you aren't successful. Not impossible, but just not likely.

Our system is corrupted by Big Money in America. The billionaires who threw million$ at the cvandidate last time and lost aren't willing to do it again.

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too much work and too expensive